Space of modular forms of level 2997, weight 1, and Character 2997.u

• Label: 2997.1.u
• Level: $2997$
• Weight: $1$
• Character orbit: 2997.u
• Rep. character: $\chi_{2997}(269,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $342$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2997 = 3^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2997.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 333 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(342\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2997, [\chi])\).

	Total	New	Old
Modular forms	30	10	20
Cusp forms	6	6	0
Eisenstein series	24	4	20

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	4	0

Trace form

\( 6 q + q^{4} - 6 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2997, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2997.1.u.a	$2997$	$1$	2997.u	333.u	$6$	$2$	$1$	$1.496$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+\zeta_{6}^{2}q^{4}-q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots\)
2997.1.u.b	$2997$	$1$	2997.u	333.u	$6$	$4$	$2$	$1.496$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots\)